Existing holographic pattern recognition systems can identify a target rapidly by matching it to information stored in the holographic template. However, such systems suffer a basic limitation in that target images must match the template exactly--in scale, rotation, and angle of view.
Disclosed in U.S. Pat. No. 4,073,010 (Casasent et al.), No. 4,084,255 (Casasent et al.), and No. 4,308,521 (Casasent et al.) are optical image processors that are distortion invariant. As described broadly in the latter patent, a space variant system in which the input scene is predistorted using coordinate transformations is provided. The idea is to predistort the input target so that the distortion which is sought to be rendered invariant manifests itself as a linear shift in the distorted coordinate system. Thus, if the input scene is mapped into polar coordinates, then a rotation of the input scene results in a linear shift in the polar coordinate space. With such a system, one can use a classical optical correlator and matched filter which is shift invariant to detect the distorted target. However, it should be appreciated that the practical implementation of the system requires a loss of some useful target information. A system which is scale and shift invariant is specifically disclosed in the first mentioned patent, while the second mentioned patent uses this technique for scale, rotation, and position invariance. It should also be appreciated that the systems are space variant and require segmentation of the input scene so that only one target is presented at any one time.
In U.S. Pat. No. 4,490,851 (Gerhart et al.), a fully digital technique for data reduction in classification is disclosed. This technique is not target specific because large amounts of target information are lost and it is also not rotation invariant.
A rotationally invariant filter is disclosed in: "Optical Pattern Recognition Using Circular Harmonic Expansion", Y. Hsu and H. Arsenault, Applied Optics, Vol. 21, No. 22, 15 Nov.1982, pp. 4016-4019. The filter is a computer-generated hologram designed to match one of the circular (Fourier) angular harmonics of the target. This filter is not target specific because only one angular harmonic is used. Such circular harmonic filters are also related to linear combination filters as disclosed in: "Optical Character Recognition Based on Nonredundant Correlation Measurements", B. Braunecker, R. Hauck, and A. Lohmann, Applied Optics, Vol. 18, No. 16, 15 Aug. 1979, pp. 2746-2753; "Unified Synthetic Discriminant Function Computational Formulation", D. Casasent, Applied Optics, Vol. 23 , No. 10, 15 May l984, pp. 1620-1627; and "Linear Combinations of Filters for Character Recognition: A Unified Treatment", H. Caulfield, Applied Optics, Vol. 19, No. 23, 1 Dec. 1980, pp. 3877-3878. This relationship is shown by "Rotationally Invariant Correlation Filtering", G. Schils and D. Sweeney, Journal of the Optical Society of America-A, 2, p. 1411 (1985). All of these references are herein incorporated by reference.